Water running through a canal at railway speeds will destroy the canal very quickly. And water in a canal is obviously unidirectional -- the canal cannot go downhill both ways.

@AlexP I explicitly said that it wouldn't run as fast as a railway. And, about going both ways - you can always build two canals. We have infinite money, afterall!

You can build two canals, but you can never build two fast-flowing canals one from A to B and the other from B to A. Water simply does not flow uphill, so that at least one of the canals will not carry $\rightarrow$flowing$\leftarrow$ water.

You don't build uphill. Those channels are straight. The fast flowing water comes from a big dam or something similar to keep the river flowing. If you have one of the sides constantly inputting water, water will flow even on a relatively straight line.

To add to what the others said, a Canal also need maintenance and erosion is a bitch

@Mermaker i am not worried about the canal being a canal, but rather that it will clog up or become a normal river, with lots of turns. A Canal is usually an artifical structure and erosion can make short work of those. There is a good video from Practical Engineering on the matter.

Concerning uphill travel: boat lifts. There are not many of them but it is possible! See en.m.wikipedia.org/wiki/Falkirk_Wheel

@PipperChip Pound locks, too. Very ancient tech!

The surface of the water definitely needs to slope downhill in the direction of travel, otherwise the water will not continue to flow. When you see a canal or river that is apparently flat, that just means it is flowing slowly and the drop in the water level is not noticeable to you. Normally this is OK because we don't expect the motion of the water to bring the boat to its destination; we use other forms of propulsion.

@AlexP My parent's walk to and from school was uphill both ways...

Why have a current? Boats have paddles/propellers. But locks are slooooow. Instead, build a network of canals at sea level, one at 512 meters, one at 1024 meters, and so on. Each city is within 256 vertical meters of a canal, which isn't so bad. Denver (1600 meters) uses the 1536 canal which is slightly underground. Boat lifts to change altitude. Panama canal will not need locks, just build the whole thing subterranean at sea level! Massive cargoship-sized aqueducts reaching into the clouds or plumbing dwarven depths are beautiful. Just don't look at the pricetag.

As this question is tagged hard science, I feel like this answer is really not realistic enough. Re: fast flowing channels in both directions here's a chapter to read if you don't believe David K and Alex P Open Channel Flow Given that you can't have any flow without either propelling the water with pumps, or a slope, it becomes more energy efficient and requires less maintenance to just propel the boats.

@Rick I'm familiar with open channel flows. That said, I'm not sure people are getting from my answer the idea I wanted to pass. It's not that I don't believe them, it's more like I couldn't explain myself properly. I'll do a rewrite on this answer when I have more time.

What happens when the water freezes?

@EvilSnack: Uphill both ways is easy, just place a ridge or valley between the endpoints. Monotonic decline, permitting flowing water, ah that's another matter entirely. (And carefully noting the difference between monotonic, monotonous, and mountainous)

@AlexP, if money is no object, you can line the canal with your choice of extremely erosion-resistant materials. There are water pipes that have survived a century or more of high-pressure water flow.

Parallel canals would technically be a track. Imagine the cargo volume!

This reminds me of the days when the most efficient method of data transmission was a plane full of CDs. Not very fast, but you could sure move a lot of bits at a time!

@MarkRansom it's still true today. Though you get better bandwidth with SDD drives and trains.

Perhaps rather than an open channel (which is what all canals built so far have been), you want a pipe, and your boat is a submarine.

Another option: an open canal, but when not in use it contains just a small amount of water in a very, very deep and narrow channel. This allows you to achieve the necessary end-to-end drop in water level while staying within the channel.